Question

if the length of a rectangular field be increased
by 4% and the breadth diminished by 10%
by how much percent will its area increase
or decrease.​

Answer 1

Answer:

6.4 %

Step-by-step explanation:

Assume the original Length = x

Original breadth = y.

Original Area = xy.

New length = x + 4% of x

$= x + \frac{4}{100}x = \frac{104}{100}x = 1.04x$

New breath = y - 10% of y

$= y - \frac{10}{100}y = \frac{90}{100}y = 0.9y$

New Area = New length × New breadth

= 1.04x × 0.9y = 0.936xy

Decrease in Area = Original - New

$= xy - 0.936xy = 0.064xy$

% Decrease =

$\frac{decrease}{original} \times 100\% \\ = \frac{0.064xy}{xy} \times 100\% \\ = 0.064 \times 100\% = 6.4\%$

Thus, the area will decrease by 6.4 %